Environmental regulations and incentives for compliance audits

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Environmental Regulations and Incentives for Compliance Audits Birendra K. Mishra, D. Paul Newman and Christopher H. Stinson

We consider the effects of two policy variables on firms' environmental compliance auditing. First, we evaluate the effect of a regulatory agency's ability to access firms' environmental reports and to penalize firms based on those internally-generated reports. In our model, the regulator's right to access unambiguously increases the incentives for firms to conduct compliance audits. Thus, recent state legislation which protects firms' compliance audits (Cushman 1996, p. A12) may be unintentionally counterproductive. Second, we consider the effect of a penalty schedule which depends on firms' good-faith efforts to detect and correct environmental non-compliance. The proposed changes to the U.S. sentencing guidelines (Anderson 1994, p. 48) incorporate this kind of conditional penalty schedule. In our analysis, the likelihood that a firm includes compliance auditing in its strategy increases as the benefit from self-detection of environmental problems increases. Thus, the proposed change in penalties appears to be capable of achieving its objective of increasing the number of firms' environmental audits. © 1997 Elsevier Science Inc.

1. I n t r o d u c t i o n T h e p u r p o s e of o u r p a p e r is to investigate the effects of two policy variables on a firm's incentives to c o n d u c t environmental compliance audits. First, we evaluate the effect of a regulatory agency's ability to access the firm's e n v i r o n m e n t a l audit r e p o r t and, subsequently, to penalize

Address correspondence to: Professor Christopher H. Stinson, Department of Accounting B6400, Graduate School of Business, The University of Texas at Austin, Austin, Texas 78712-1172, USA; E-mail: [email protected]. Journal of Accounting and Public Policy, 16, 187-214 (1997) © 1997 Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010

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the firm based on that internally-generated report. Second, we evaluate the incentive effect of a penalty schedule which depends on a firm's good-faith efforts to detect and correct environmental non-compliance. Businesses in the United States and many other countries are subject to many environmental laws and regulations. Because these laws are detailed and complex, compliance audits are used to determine whether a company's internal control systems are keeping the firm in compliance with environmental laws (CH2M Hill 1993, p. 6; Schaltegger and Stinson 1994, p. 15). 1 Compliance audits are usually undertaken by teams with knowledge of engineering, chemistry, and environmental law (Morelli 1994, p. 104). Several benefits accrue to the company from undertaking compliance audits. Firms may be able to identify environmental problems early and thereby reduce cleanup costs associated with environmental remediation. 2 Firms may have an internal commitment to being environmentally responsible; compliance audits provide an opportunity to identify points where this social commitment is not being achieved. Insurance companies may offer lower rates to businesses which can demonstrate that their internal control systems are adequate for monitoring the firm's compliance with environmental laws. Regulators, such as the Environmental Protection Agency (EPA) and U.S. Department of Justice (DO J), publicly encourage firms to conduct environmental compliance audits. Additionally, proposed U.S. sentencing guidelines allow sentencing leniency for certain corporate crimes only if firms can demonstrate that they had programs in place designed to reduce the possibility of the discovered crimes (Anderson 1994, p. 48). As an example, an existing program of compliance audits would be necessary for lenient treatment of corporations and managers found guilty of fraudulent environmental activities (Manko and Gilsford 1991/1992, p. 226; Anderson 1994, p. 48). Finally, the International Standards Organization is developing compliance audit standards as part of ISO 14001 (Tibor and Feldman 1996, pp. 47-48). If these audit standards become as widely accepted as the ISO 9000 Total Quality Management standards, some customers (e.g., European governments) may require that firms be certified as having appropriate environmental audit programs before business is conducted (Tibor and Feldman 1996, pp. 30-31).

1 In this paper, we focus exclusively on c o m p l i a n c e audits. C o m p l i a n c e audits c a n be distinguished f r o m two o t h e r kinds of e n v i r o n m e n t a l a u d i t s - - o p e r a t i o n a l audits a n d due-diligence audits. O p e r a tional audits generally focus on the m a n a g e r i a l issues of efficiency a n d effectiveness, a n d include waste-minimization audits. Due-diligence audits are reviews of the potential e n v i r o n m e n t a l liabilities associated with s o m e business asset, such as c o r p o r a t e - o w n e d real estate, a firm's waste stream, or an entire business division (see C H 2 M Hill 1993, pp. 6 - 9 ; Schaltegger a n d Stinson 1994, pp. 1 4 - 1 6 for a discussion of these definitions). Ten a r e a s of benefits are identified by Campbell a n d Byington (1995, p. 15). The benefit r a n k e d highest by c o r p o r a t e r e s p o n d e n t s to a survey by C a m p b e l l a n d Byington (1995, p. 15) is "early identification of p r o b l e m s before r e g u l a t o r y action."

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A number of disincentives for voluntary compliance audits also exist. First, the direct cost of such audits in terms of expert personnel may be substantial (Campbell and Byington 1995, p. 16). Second, many firms argue that environmental audits create a substantial risk of self-incrimination because many regulators (e.g., the EPA and DO J) have the legal right to inspect the results of voluntary compliance efforts (Campbell and Byington 1995, p. 16).3 Not surprisingly, even firms which make genuine efforts to comply with all environmental regulations occasionally find that they have failed to comply with all laws at all past times (e.g., CH2M Hill 1993, p. 18). Information acquired by firms during a compliance audit can be accessed by the EPA or DOJ and used to penalize firms and their management. Regulators can fine a company just as harshly when violations are discovered by internal compliance audits as they can if the regulator is the original discover of the violation (Moore 1992, p. 40). If the information becomes public, firms also can be sued by third parties in tort liability suits. Thus, regulatory access to compliance audit results may create substantial disincentives for firms to undertake such audits (Moore 1992, p. 40). In attempting to address this incentive problem, the EPA and DOJ had indicated that, as a matter of regular practice, they will not seek out environmental audit results (EPA 1995a, p. 25007). However, the EPA and DOJ still reserve the right to request compliance audit results if such are ever deemed to be of interest (EPA 1995a, p. 25007). Therefore, it is not clear whether these federal guarantees actually alleviate the incentive problem associated with compliance audits. As of mid-1996, at least 18 states had passed laws that among other things limited regulatory access to voluntary compliance audits (Cushman 1996, p. A1). Legislatures and environmental regulators in several other states are considering similar proposals (Cushman 1996, p. A12). The EPA has expressed concern that these bills will reduce firms' incentives to comply with environmental laws (EPA 1995b, p. 66707). Consequently, since mid-1995, the EPA has sent warning letters to five states (Arizona, California, Florida, Idaho, and Ohio) threatening to revoke federallygranted authority for state-level enforcement of the federal Clean Air Act if such proposals become state law ("Enviro auditing: EPA opposition squelches some state bills" 1996, p. 1). Similarly, the Michigan Department of Environmental Quality is concerned that EPA may revoke some of Michigan's environmental regulatory authority because of EPA's concerns about Michigan's audit-protection ("Michigan: State firms cite high enviro

3 O f the types of e n v i r o n m e n t a l audit costs identified in C a m p b e l l a n d Byington (1995, p. 16), c o r p o r a t e r e s p o n d e n t s of their survey indicated t h a t " u s e of audit r e p o r t s against c o m p a n y in r e g u l a t o r y a c t i o n " r a n k e d first in risk a n d " s u b s t a n t i a l p e r s o n n e l costs" r a n k e d second. In a survey by Price W a t e r h o u s e ( " C o m p a n i e s wary of use of e n v i r o n m e n t a l a u d i t s " 1995, p. 25) c o m p a n i e s claimed t h a t they " w o u l d c o n d u c t m o r e e n v i r o n m e n t a l audits if they were a s s u r e d the results w o u l d not be u s e d to penalize t h e m . "

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compliance costs" 1997, p. 18). Possibly in response to the EPA's discouragement, not all states have allowed similar, proposed bills to become law (see, e.g., "Florida: Biz self-audit bill stalls, but may come up again" 1996). Subsequently, the EPA (1995b, p. 66706) announced a new policy which became effective in January 1996, to "promote compliance with environmental laws by providing businesses with substantial incentives (e.g., reduction or elimination of civil penalties) to voluntarily disclose and correct environmental violations. ''4 This new policy will not apply to firms with a history of violations or to violations creating "an imminent and substantial endangerment or serious actual harm to public health or the environment" (EPA 1995b, p. 66707). As of early May 1996, 65 companies had reported self-discovered environmental violations to the EPA in response to this new policy; nonetheless, several U.S. Senators have proposed federal standards which would be even more lenient than this new EPA policy (Fairley 1996, p. 13). The firm, in evaluating its environmental audit program, must balance these various incentives, including the direct cost of the audit and the incremental expected cost of penalties due to the regulator's ability to access the firm's potentially incriminating audit versus the reduced cleanup cost due to early detection of environmental problems and (potentially) the reduced penalty from a good-faith effort to prevent or clean up environmental violations.5 The regulator, on the other hand, must balance the direct costs of accessing the firm's audit results and the direct cost of a separate investigation versus the expected undetected environmental damage caused by the firm. The interaction of these parties determines the extent of compliance auditing and the effects of any regulatory policy change. In the ensuing sections, we will investigate the strategic interaction between environmental regulators and a firm considering a compliance audit. We will investigate how the optimal strategy of the firm (i.e., whether to undertake compliance audits voluntarily) varies with two policy variables: (1) the ability of a regulatory agency to access the firm's environmental audit report and penalize the firm based on that report, and (2) penalties for environmental violations which are (or are not) reduced if a firm has a compliance audit program in place. The purpose of investigating these two scenarios is to contribute to the current policy debate

4 Additionally, several c o m m e n t a t o r s have suggested t h a t the p r o p o s e d federal s e n t e n c i n g guidelines will reduce the disincentive to u n d e r t a k e voluntary c o m p l i a n c e audits ( A n d e r s o n 1994, p. 47; Doyle 1992, p. 39, M o k h i b e r 1995, p. C l l ) . 5 E n v i r o n m e n t a l n o n - c o m p l i a n c e m a y o c c u r in a variety of circumstances. F o r example, a single n o n - r e c u r r i n g spill m a y t a k e place a n d detection m a y o c c u r s o m e time later. In this case, early detection m a y have little positive benefit to the firm. Alternatively, pollution m a y be c a u s e d by a process which is out of control a n d will r e m a i n out of control until detected. In this case, early detection r e d u c e s the c l e a n - u p cost to the firm. O u r analysis primarily focuses o n the latter case.

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regarding (1) whether the results of voluntary compliance audits should be accessible to environmental regulators, and (2) whether the proposed U.S. sentencing guidelines will alleviate the disincentives to undertake compliance audits. Section 2 of this paper presents the model and its assumptions, and describes the payoff functions of the firm and the regulator. Section 3 describes the equilibria of various settings. Section 4 directly addresses the two policy questions described above, and Section 5 contains our conclusions.

2. Model We consider three scenarios in a single-period compliance game. First, we develop a setting in which a regulatory agency (hereafter, the regulator) has the authority to access the firm's environmental audit report; possible P~rtnalties for detected non-compliance are independent of the firm's efs. This setting is the benchmark model. In the second setting, we assume that the regulator cannot access the firm's audit report, but that penalties for non-compliance are again independent of the firm's efforts. Finally, in the third setting, we allow the regulator to access the firm's audit reports, but assume that penalties for detected non-compliance are reduced if the firm has made a good-faith effort to audit and correct environmental deficiencies. In modeling these settings, we wish to construct representations of incentives and strategies which are as simple as possible, while retaining the tradeoffs discussed in the introductory section. We assume the firm balances the benefit of compliance audits (e.g., reduction of expected cleanup costs) against both the direct costs (e.g., personnel) and the costs of self-incrimination if the regulator accesses. Similarly, the regulator balances the reduced social cost of environmental damage against both the cost of accessing the firm's audit and the direct cost of inspections. The time line of events is in Figure 1. First, nature selects the firm's type, i.e., whether the firm is in compliance (with probability 1 - /3) or out of compliance (with probability /3) with environmental regulations.6 Neither the firm nor the regulator observes the firm's type initially. The firm may either conduct a compliance audit or not, denoted a I and a 2, respectively. Let a denote the probability that the firm chooses a 1 (com-

6 A m o r e complex setting w o u l d allow the firm to select its level of c o m p l i a n c e a n d t h e n decide w h e t h e r to c o n d u c t a c o m p l i a n c e audit. In o r d e r to focus o n the effects o f r e g u l a t o r y access a n d differential penalties on a u d i t choice alone (as have m a n y of the public debates), we assume that the likelihood of c o m p l i a n c e is r a n d o m a n d b e y o n d the control of the firm.

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I ....................

Nature seleds

firm type

I ...............

F i r m chooses a u d i t o r n o audit

I ......................

I ......................

I

Regulator cho~

Regulator chooses

Payoffs

access o r n o access

inspect o r n o inspect

r~dlzed

Figure 1. Time line of events.

pliance auditing). We assume that if conducted, a compliance audit detects non-compliance with certainty, after which the firm corrects the problem. 7 We also assume that the audit never detects non-compliance falsely. Subsequent to the firm's action, the regulator can perform an independent inspection to check if the firm is in compliance or non-compliance/ In the benchmark model, before conducting any inspection, the regulator can choose to obtain information about the firm's compliance audit. The regulator has three possible strategies at this stage. The regulator can choose to: (1) access the finn's audit report and condition its inspection policy on the outcome of its access; (2) not access the firm's audit report and conduct an independent inspection; or (3) not access the firm's audit report and not conduct an independent inspection. We denote these strategies sl, s 2 and s 3, respectively. Let 8j denote the probability that the regulator adopts strategy sj, where E}= 16y = 1. If the regulator accesses the firm's compliance audit report, it learns whether the firm has conducted a compliance audit and the outcome of that audit. 9 Thus, depending on the firm's strategy, the accessing regulator is in one of two information sets. Let pl denote the accessing regulator's probability of inspection when the firm has conducted a compliance audit, and p: be the accessing regulator's probability of inspection when the firm has not conducted a compliance audit.

2.1 Costs and Penalties Cf denotes the firm's cost of a compliance audit, and C O is the firm's clean-up cost (including the cost of corrective action) when the firm

7 T h e a s s u m p t i o n t h a t c o m p l i a n c e audits are perfect is a n obvious simplification in o u r model a n d reflects o u r focus on policy variables (i.e., the a u t h o r i t y to access reports a n d a conditional penalty schedule) r a t h e r t h a n on a u d i t technologies. In addition, we assume that the firm always corrects a n y d e t e c t e d n o n - c o m p l i a n c e . Implicit h e r e is the view t h a t expected penalties, including indirect costs such as adverse publicity, for not c o r r e c t i n g known n o n - c o m p l i a n c e always exceed the firm's cost o f correction. 8 F o r s e m a n t i c clarity, firms audit themselves, while the r e g u l a t o r inspects firms to ascertain the firm's compliance. In using these terms, we envision similar objectives a n d activities. Consistent with o u r a s s u m p t i o n r e g a r d i n g the firm, we assume t h a t the r e g u l a t o r ' s inspection technology is perfect, a l t h o u g h the cost of investigation m a y differ for the firm a n d the regulator. 9 W e d o n o t address issues of firm credibility in o u r model, as the policy d e b a t e has ignored such issues. If the firm's self-audits a r e not credible, t h e n the r e g u l a t o r c a n learn n o t h i n g f r o m t h e m , a n d there is n o benefit to the r e g u l a t o r (or cost to the firm) to accessing. Presumably, penalties associated with false r e p o r t s are quite severe, thus inducing firms to provide correct information.

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detects non-compliance and corrects it. If non-compliance occurs but the firm does not audit (and, so, does not correct the problem), the cost of correction and clean up increases to Dy(Dy > Co) due to the additional environmental damage. 1° Similarly, the regulator's cost of inspection is Cr and the regulator'scost of accessing the firm's audit report is K. 11 The regulator's estimate of the cost of environmental damage is D r. The costs associated with the same amount of damage can be different for the firm and regulator, as the cost to the firm is the monetary cost of clean-up, but the regulator additionally may impute the cost of negative social consequences in its assessment of environmental damages. We consider two different penalty structures. The first, called the unconditional penalty structure, corresponds to the penalty structure currently in place (Anderson 1994, p. 47). In the unconditional penalty structure, the regulator treats any detected non-compliance on the part of the firm with equal severity regardless of whether the firm discovered and corrected the problem (detected by accessing the firm's report) or the regulatory agency discovered the non-compliance by independent inspection. Let V0 be the penalty imposed in either case. Alternatively, under the proposed federal sentencing guidelines, any good-faith efforts by the firm are considered when the penalty is assessed (Anderson 1994, p. 48). Thus, if the firm has audited and corrected its non-compliance, the firm's penalty is reduced. Under the proposed sentencing guidelines, Va is the penalty imposed when the firm has detected and corrected the problem (Va < 110). However, if the firm has not conducted a compliance audit and the regulator detects non-compliance, then the firm has to pay the higher penalty, V0, as before. We call this proposed penalty policy the conditionalpenalty structure, reflecting its dependence on the firm's action. To aid in the subsequent model development, Table 1 provides a summary of our notation.

2.2 Expected Costs--Benchmark Scenario (Regulatory Access and Unconditional Penalty) In all of the scenarios we consider, the firm's objective is to minimize the total expected costs of non-compliance (clean-up and penalties) and com1°By a s s u m i n g D f > C 0, we c a p t u r e the h i g h e s t - r a n k e d benefit of c o m p l i a n c e audits, early identification of e n v i r o n m e n t a l p r o b l e m s (see f o o t n o t e 2). As we show later, no compliance audit will o c c u r in the b e n c h m a r k model (with r e g u l a t o r y access a n d u n c o n d i t i o n a l penalty) if D f = C 0, b e c a u s e t h e r e is n o net benefit to the firm f r o m such a n audit. 11 T h e cost of accessing c a n include b o t h direct costs (e.g., h o u r s devoted to r e a d i n g a n d c o m p r e h e n d i n g the r e p o r t ) a n d indirect costs (e.g., legal expenditures to overcome challenges the firm may u n d e r t a k e to block the r e g u l a t o r ' s right to access). W i t h o u t an explicit cost of accessing, the r e g u l a t o r ' s strategy obviously w o u l d b e to access all reports. B e c a u s e we do not observe such b e h a v i o r in practice, we a s s u m e t h a t accessing imposes some cost o n the regulator.

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Table 1. Summary of Notation Parameters /3 = Cf = CO = Df = V0 = V~ =

Probability that the firm is out of compliance. Firm's audit cost. Firm's clean-up cost if firm audits. Firm's clean-up cost if firm does not audit. Firm's penalty if detected out of compliance by regulator. Firm's penalty if detected out of compliance by regulator and firm has voluntarily audited (Scenario 3 only). C r = Regulator's inspection cost. K = Regulator's accessing cost. Dr = Regulator's assessment of damage cost. Strategy elements c~ = 61 = 82 = 63 = Pl = P2 =

Firm's probability of auditing. Regulator's probability of accessing. Regulator's probability of not accessing and inspecting. Regulator's probability of not accessing and not inspecting. Given access, regulator's probability of inspecting if the firm has audited. Given access, regulator's probability of inspecting if the firm has not audited.

y = Regulator's probability of inspecting given that accessing is unavailable (Scenario 2 only).

pliance audit costs. Similarly, the regulator minimizes the total expected costs of: (1) accessing the firm's audit report; (2) independent inspection; and (3) the undetected damage due to the firm's environmental non-compliance. We assume that the regulator does not consider the amount of imposed penalties when selecting a strategy. 12 First, we consider the benchmark scenario, in which there is regulatory ability to access the firm's audit report and an unconditional penalty for detected non-compliance. To simplify subsequent representations of expected costs, we initially demonstrate a straightforward and intuitive result: when the firm audits and the regulator accesses the firm's audit report, the regulator does not inspect. Lemma 1. When the firm has conducted a compliance audit and the regulator

accesses the firm's audit report, the regulator does not inspect, i.e., Pl = O. (All proofs are in the Appendix.)

12 While the amount of penalties collected may be relevant to the legislative policymaker, we do not view the regulator as directly benefiting by raising more revenues through fines. In particular, if collected penalties were included as a measure of an environmental regulator's effectiveness, the regulator may be induced to discourage self-audits because fines collected are greater if the firm does not detect environmental problems itself. This incentive effect seems to contradict the regulator's espoused objective of minimizing environmental damage.

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By accessing the firm's audit report, the regulator knows that the firm either has no violations or has already detected and corrected any noncompliance. Because the firm is in compliance at the time of the regulator's access, any additional inspection effort by the regulator is unnecessary and inefficientJ 3 Hence, the regulator does not inspect. When the regulator accesses the firm's compliance audit report, its subsequent action may include an inspection only if the firm has not already conducted a compliance audit. Given that the regulator does not conduct an inspection when it accesses and the firm audits, the expected costs for the regulator for its three different strategies are: Access: E R I s I = a K + (1 - a ) [ K

= K + (1

-

CrP 2 "+ ~3Dr(1 -

+

p2 )]

tx)[CrP 2 + ~3Dr(1 - P2)];

No access, inspection: E R I s 2 = C r a ( 1 - /3) + Cra/3 + Cr(1 - a ) ( 1 - / 3 ) =

+ Cr(1 -- Or)~3

Cr;

No access, no inspection: E R I s 3 = a(1 - /3)(0) + a/3(0) + (1 - a ) ( 1 - /3)(0) + ~3Dr(1 - a ) = ~3Dr(1 - a ) .

Here E R [ s j is the regulator's expected cost given that the regulator is following strategy sj. For example, the access expected cost, E R ] s a, is composed of three elements: the cost of accessing (K), the expected cost of inspection ((1 - a)p2Cr), and the expected undetected pollution damage ((1 - a)(1 - p2)/3Dr). Recalling that 6/denotes the probability that the regulator uses strategy sj, the (unconditional) expected cost to the regulator is given by: E R = 81K + 81(1 - a)[C,.p2 + / 3 D , ( 1 - P2)] -~- 8 2 C r --[- ( 1 -

81 -

82)/3Dr(1 - a ) .

(1)

In order to focus on the tradeoffs of accessing and inspecting, the regulator's expected cost described in equation (1) can be rearranged as follows: E R = {6aK} + {[81(1 +{[81(1

-

-- P2) +

or)p2 +

82]Cr}

1 - - 81 -- 8 2 ] ( 1

-- a)/3Dr}.

13After non-compliance is corrected, the firm is in a state of compliance.

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The first bracketed term represents the expected cost of accessing, the second is the expected cost of inspecting, and the third is the expected cost of undetected environmental damage. The expected costs to the firm for auditing (a 1) and not auditing (a 2) are: EF[a 1 = Cf + tiC o + [3 61V0 -4- [3 ~2Vo and E F I a 2 = [3[ p 2 6 , ( D / + V0) + 62(Dr + Vo)]. For example, the firm's expected cost from auditing, E F l a ~, is composed of four elements: audit cost (C/); expected clean-up cost (/3C0); expected penalty if the regulator accesses times the probability that the regulator will access (/3 6Y0); and expected penalty if the regulator does not access but conducts an independent inspection times the probability of that strategy ( [3 62V0). Denoting the probability of auditing by a, the (unconditional) expected cost to the firm is given by: EF = a[Cf + [3C o + [361Vo + /362Vo] +(1 - a)[3[ p261(Df + Vo) + 62(Df + V0) ].

(2)

Rearranging equation (2) to emphasize the tradeoffs made by the firm, yields: EF = {o~Cf} A- {ot/3C 0 -f- (1 -- ot)/3(p261 + 62)Dr} +{[3Vo[a(,~l + 62) + (1 - a)(p26~ + 62)]}. The first bracketed term is the expected audit cost, the second is the expected clean-up cost, and the third is the expected penalty. 2.3 Expected Costs--Scenario 2 (No Regulatory Access and Unconditional Penalty) In scenario 2, the regulator cannot access the firm's compliance audit report and thus cannot determine whether the firm audited. Therefore, the setting loses its sequential nature and can be modeled as a simultaneous game. The firm can conduct a compliance audit or not, and the regulator can inspect or not (but is unable to access any existing audits). This scenario corresponds to the conditions which would result from denying environmental regulators access to firms' environmental audits (e.g., as advocated by Moore 1992, p. 41). Let a and y denote the probability of audit by the firm and inspection by the regulator, respectively, The expected cost to the regulator is: ER = TC~ + (1 - y)(1

-

o t ) f l D r.

(3)

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The regulator's expected cost is composed of two elements: the expected cost of inspection (yCr), and the expected undetected pollution costs ((1 - T)(1 - a)flDr). The expected cost to the firm is given by: EF = a ( C f + tiC o + /3"),V0) + (1 - a)[3T(O f + V o)

(4)

or, rearranged, EF = {aCf} + {ct[3Co + (1 - ct)[3yDf} + {/3yV0}.

The firm's expected cost is composed of three elements: expected audit cost ( a C f ) , expected clean-up cost (t~/3C o + (1 - a)flyDf), and the expected penalty (/3yV0). 2.4 Expected C o s t s - - S c e n a r i o 3 (Regulatory Access and Conditional Penalty)

In scenario 3, we capture the essence of the proposed federal sentencing structure where the non-compliance penalty is reduced based on good-faith prevention efforts by the firm. Otherwise, this scenario is identical to the benchmark setting because regulatory access to the firm's audit report is retained. Here, the firm faces the penalty V0 if the firm is out of compliance and the regulator finds the non-compliance by independent inspection. However, if the firm has conducted a compliance audit and corrected the problem, then the alternate penalty, Va, is assessed, where

Va
and g r l a 2 = fl[ PE~l(Of + V O) + ~2(Of + V0)] •

The (unconditional) expected cost to the firm is given by: EF = a[Cf + 13Co + fl 61Va --F •

62Va]

+(1 - a ) f l [ p261(Df + V o) + 62(D f + V0) ].

(5)

The first term in equation (5) is the expected cost when the firm conducts a compliance audit and may incur the reduced penalty, Va. The second term is the expected cost when the firm does not conduct a compliance audit and the penalty V0 may be incurred.

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3. Equilibria 3.1 Scenario 1 - - B e n c h m a r k M o d e l (Regulatory A c c e s s a n d Unconditional Penalty)

In the benchmark model, the firm acts first, and the regulator can access the firm's compliance audit information. Thus, the game has a sequential information structure. In the following proposition, we identify perfect Bayesian equilibria (Fudenberg and Tirole 1991, pp. 324-326).

Proposition 1. In the benchmark model where the regulator has access to the firm's compliance audit report, the following perfect Bayesian equilibria

exist: 14 (i) High inspection cost. 15 I f C r > [3D,, then 81 = 8 2 = tz = 0 and 8 3 = 1. That is, the firm does not audit, and the regulator does not access or inspect. (ii) L o w inspection cost, high audit cost. f f C, < flD, and Cf > [3(Df - Co), then 8 x = 8 3 = ot = 0 and 8 2 = 1. That is, the firm does not audit, and the regulator does not access but always inspects, t6 (iii) L o w inspection cost, low audit cost, high access cost. I f C, < riD,, C/ < [3(Df - C 0) and K > C,( flD, - Cr)/flD,, then 82 = (Cf + [3Co)/[3D/, 81 = O, 8 3 = 1 - 8 2 , and a = 1 - Cr/[3D r. That is, the firm mixes between auditing and no-auditing, and the regulator mixes between [no-access, no-inspect] and [no-access, inspect]. (iv) Low inspection cost, low audit cost, low access cost. I f C, < [3D,, C: < [3(D: - Co), and K < C,( riD, - C,)/[3D,, then P l = O, P2 = 1, 81 = ( C f + f l f o ) / [ 3 D f, ~2 = O, ~3 -~- 1 -- ~1 and a = 1 - K / ( [3Dr - Cr). That is, thefirm mixes between auditingand no-auditing, and the regulator mixes between [access; no-inspect I audit, inspect lno-audit] and [no-access, no-inspect]. For each equilibrium for which the regulator does not access (i.e., (i), (ii), and ( iii)), the regulator's out-of-equilibrium beliefs (if it accessed) regarding the firm's type are that the firm is in compliance with probability 1 - fl, if

14 W e c o n s i d e r only conditions with strict inequalities b o t h in the s t a t e m e n t s of Propositions 1, 2, a n d 3, a n d in the proofs. Conditions with equalities result in strategic indifference by the regulator, the firm, o r both. W e view these cases as unlikely a n d relatively uninteresting. 15 While we chose, for exposition, to c h a r a c t e r i z e this equilibrium as high inspection cost, the t e r m high is relative to the r e g u l a t o r ' s expected e n v i r o n m e n t a l d a m a g e from n o n - c o m p l i a n c e . This caveat applies to the descriptors we apply to e a c h equilibrium. 16 Note t h a t if Df = C o, the firm will not audit in the b e n c h m a r k setting b e c a u s e Cf > 0. Thus, if the pollution event is a o n e - t i m e o c c u r r e n c e a n d c l e a n - u p costs d o not increase over i i m e , the firm has n o incentive to audit.

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the firm has not audited, certainty that the firm is in compliance if the firm has audited and detected no non-compliance, and certainty that the firm is out of compliance if the firm has audited and detected non-compliance. 17 The four equilibria span the parameter space, implying that one of these equilibria exists for any parameter values. The first equilibrium is a pollution equilibrium, which occurs when the regulator's inspection cost is relatively high compared to expected damages from pollution (C r > /3Dr). As the regulator never inspects in this equilibrium, the firm has no incentive to do a compliance audit. This equilibrium characterizes any setting with a firm having a comparatively low likelihood of polluting the environment or for which the extent of potential damage is small. The second equilibrium is characterized by relatively high damages to the environment compared to the regulator's inspection cost (C, < /3D,). In this case, the regulator always inspects because the benefit is high compared to the regulator's inspection cost. The firm does not audit because the firm's audit and clean-up costs are greater than the expected clean-up costs, given detection by the regulator ( C / + [3Co > [3Dr). This equilibrium features a regulator with relatively efficient environmental audit technology (compared to the firm's technology) or significant differences in the two assessments of environmental damages (D r versus Dr). The third and fourth equilibria are more interesting because they do not represent always-inspect or never-inspect regulatory strategies. In the third equilibrium, the regulator mixes between {no-access, inspect} and {noaccess, no-inspect} strategies due to the relatively high cost of accessing (K > Cr( [3D, - C~)/[3Dr). In response, the firm mixes between auditing and no-auditing. In the fourth equilibrium, the regulator's inspection cost is low compared to expected damages to the environment (C~ < /3D~). The regulator mixes between {access} and {no-access, no-inspect} strategies due to the relatively low cost of accessing (K < Cr( [3D~ - C~)/[3D~). For the firm, the cost of an audit is less than the expected cost savings from an audit (Cf + [3Co < [3Dy), but because the regulator does not always inspect, the firm, in turn, mixes between auditing and no-auditing. TM Notice that when there is an unconditional penalty for polluting, V0, whether or not the firm has conducted a compliance audit, the penalty has no effect on the strategies of either the firm or the regulator. In addition,

17 T h e s e o u t - o f - e q u i l i b r i u m beliefs arise naturally a n d intuitively. If the r e g u l a t o r accesses a n d observes n o audit, it c a n l e a r n n o t h i n g by its access; thus its post-access beliefs are u n c h a n g e d f r o m its p r i o r beliefs. If the r e g u l a t o r accesses a n d the firm has audited, the r e g u l a t o r learns perfectly w h e t h e r the firm was in c o m p l i a n c e or o u t of compliance. ~s N o t e t h a t the r e g u l a t o r n e v e r uses the p u r e strategy always-access in equilibrium, regardless of how inexpensive accessing m a y be relative to inspecting. If the r e g u l a t o r always accessed, the firm w o u l d always a u d i t in response, m a k i n g access u n n e c e s s a r y .

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in either mixed strategy equilibrium ((iii) or (iv)), the regulator's strategy is independent of its inspection cost or the environmental pollution cost. Similarly, the firm's strategy is independent of the firm's audit cost or clean-up cost. 3.2 Scenario 2 - - N o Regulatory Access a n d Unconditional Penalty

The following proposition characterizes possible Nash equilibria of the model (Fudenberg and Tirole 1991, pp. 11-14) with no regulatory access to the firm's compliance audit. Proposition 2. In the model where the regulator has no access to the firm's compliance audit report, the following Plash equilibria exist: 19 (i) High inspection cost. I f C r > [3Dr then T = a = O. That is, the firm does not audit, and the regulator does not inspect. (ii) L o w inspection cost, high audit cost. I f C r < flD r and Cf > [3(Df - Co), then T = 1 and a = O. That is, the firm does not audit, and the regulator always inspects. (iii) L o w inspection cost, low audit cost. I f C r < flD r, Cf < fl(Df - Co), then Y = (Cf + flCo)/[3D f and a = 1 - C r / f l D r. That is, the firm mixes between auditing and noauditing, and the regulator mires between no-inspection and inspection. The first equilibrium is the pollution equilibrium similar to the first equilibrium in the benchmark setting. This outcome occurs when the regulator's inspection cost exceeds the expected pollution cost (Cr > /3Dr)Neither the firm nor the regulator conducts an investigation. The second equilibrium is similar to the second equilibrium in the benchmark setting. In this equilibrium, the regulator inspects with certainty, and the firm never audits because auditing is costly relative to its benefits (Cf + fl(C 0 - D/) > 0). The third and only mixed strategy equilibrium for the no-access case is equivalent to the third equilibrium in the benchmark setting. Although access is allowed in the benchmark setting, the regulator never accesses the firm's audit report in equilibrium (iii). Accessing is either too costly relative to inspection (so the regulator inspects) or accessing is so inexpensive relative to inspection that the firm (anticipating access) audits, thus making access unnecessary. Proposition 2 contains no equivalent to equilibrium (iv) in the benchmark setting, as the regulator includes accessing in

19 S e e f o o t n o t e 14.

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its strategy in that equilibrium. As in the benchmark case, the undonditional penalty has no effect on the equilibrium strategy of either the, firm or the regulator. 3.3 Scenario 3 - - R e g u l a t o r y Access a n d Conditional Penalty

The following proposition characterizes perfect Bayesian equilibria for the setting with regulatory access and a penalty conditional on the efforts of the firm.

Proposition 3.

In the setting with access and a conditional penalty structure, the following perfect Bayesian equilibria exist: 2°

(i) High inspection cost. I f C r )" ilL),, then 61 = 6 2 = Ol = 0 and 6 3 = 1. The firm does not audit, and the regulator does not access or inspect. (ii) Low inspection cost, high audit cost. I f Cr < [3Dr, and C r > [3[Dr - Co + (Vo - V~)], then 6 1 = 63 = a = 0 and 62 = 1. The firm does not audit, and the regulator does not access but always inspects. (iii) Low inspection cost, low audit cost, high access cost. I f C r <( riD,, Cf < [3[Dr - C O + ( V o - Va)], and K > Cr( [30 r Cr)/[3Dr, then 6 2 = ( C f + [ 3 C o ) / / [ 3 ( V o - V a + Dr), 61 = O, 6 3 1 - 62 and ot = 1 - Cr/[3D r. The firm mixes between auditing and no-auditing, and the regulator mixes between [no-access, no-inspect] and [no-access, inspect]. (iv) L o w inspection cost, low audit cost, low access cost. I f C r < [3Dr, Cf < [3[Dy - C O + ( V o - Va)] , and K < Cr( [3Dr Cr)/[3D~, then Pl = O, P2 = 1, 61 = (C I + [3Co)/[3(Vo - Va + DI), 6 2 = O, 6 3 ~" 1 - - 61 and a = 1 - K / ( [3Dr - C,). The firm mixes between auditing and no-auditing, and the regulator mixes between [access; no inspect laudit, inspect lno audit] and [no.access, no-inspect]. For each equilibrium for which the regulator does not access (ie., (i), (ii), and ( iii)), the regulator's out of equilibrium beliefs (if it accessed) regarding the firm's type are probability 1 - [3 that the firm is in compliance if the firm has not audited, certainty that the firm is in compliance if the firm has audited and detected no non-compliance, and certainty that the firm is out of compliance if the firm has audited and detected non-compliance.

Here, we compare the equilibria for the conditional penalty setting with the benchmark setting. First, the conditional penalty schedule does not 2o See footnote 14.

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change the number or basic nature of the equilibria. The first equilibrium of the new game is identical to the pollution equilibrium of the benchmark setting. In both settings, neither the regulator nor the firm conducts an investigation. Hence, a change in the penalty structure has no effect on this equilibrium. The strategies of the firm and the regulator are also identical in the second equilibrium; however, the set of parameter values for which this equilibrium occurs differs across the two settings. The third and fourth equilibria are both mixed-strategy equilibria as in the benchmark model, with the firm's probability of compliance auditing being identical in both scenarios. We provide a more detailed comparison of these settings in the next section.

4. Policy Implications In this section, we analyze the effects of changes in policy variables on the equilibrium behavior of the firm and the regulator.

4.1 Effect o f Accessing The effects of regulatory access to the firm's compliance audit report can be assessed by comparing equilibria in scenarios 1 and 2. Note that only in equilibrium (iv) in Proposition 1 does the regulator access. Thus, for parameter values supporting other equilibria, the right to access has no effect on the behavior of the firm or regulator. For this reason, we focus on settings in which accessing the firm's audit report can have an impact on the firm's incentives to conduct such audits. Corollary 1. Assume Cr < ~D r, C / < ~(Df - C o) and K < Cr( ~Dr Cr)/13D ~ (equilibrium (iv) in Proposition 1 or equilibrium (iii) in Proposition 2 occurs). Then the regulator's right to access the compliance audit report provides a positive incentive for compliance auditing by the firm. That is, the probability of compliance auditing in equilibrium (iv) in the benchmark setting (Proposition 1) is strictly greater than the probability of compliance auditing in equilibrium (iii) in the no-access setting (Proposition 2). Note that the probability that the regulator inspects in the no-access setting (equilibrium (iii)) is identical to the probability that the regulator accesses in the benchmark setting (equilibrium (iv)), 3' = ~1. That is, when accessing is unavailable, the regulator modifies its audit policy so that the likelihood that non-compliance will be detected by the regulator is unchanged from the benchmark setting. However, if accessing is unavailable, the firm modifies its equilibrium response to the new incentive structure of

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the regulator. In particular, changes in the likelihood of auditing alter both expected costs and benefits of access/inspection strategies for the regulator in the benchmark scenario, but only the expected benefits of inspection in the no-access scenario. As a result of the interaction, the firm increases its audit probability for the access equilibrium. A comparison of Figures 2 and 3 illustrates the results of Corollary 1. Each region in Figure 2 corresponds to an equilibrium described in Proposition 1, where region I corresponds to equilibrium (i), II to (ii), and so on. Thus, when the regulator's inspection cost is high (region I, where C r > /3Dr), the regulator does not inspect and the firm does not audit. A comparison of the two figures reveals that for intermediate ranges of inspection costs (relative to accessing costs), the regulator chooses to (probabilistically) access (i.e., region IV occurs). In region IV, the regulator accesses and is better off because accessing is more efficient than in region III (equilibrium (iii) with no accessing). If inspection costs are very low relative to access costs, then the accessing strategy will not be used by the regulator. Similarly, if inspection costs are very high relative to access costs then, again, the accessing strategy is not viable because the firm would react to a very high probability of accessing by always auditing (thereby giving access zero value). In region IV of Figure 2, inspection costs are moderate relative to accessing costs, making accessing a viable strategy; because the firm's audit costs are relatively low, it is optimal for the firm to (probablisticaUy) conduct compliance audits. Two features of our setting are important in deriving the results of Corollary 1. First, access must be available to the regulator and, second,

Cf

(auditcost) lI

o o o o o

e

0

e o o o #

m~NMn~O~m~mO~OUu|o~II~WN~I~OOO~Hqm~|n~OONOM~

~Dr Figure 2. Equilibrium regions for Scenario 1.

C r (inspection cost)

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Cf i (audit cost)

d

II

IH

J

J

e e

P 13Dr

C r (inspection cost)

Figure 3. Equilibrium regions for Scenario 2.

access must be efficient (but not too efficient). In the efficient range of access cost, the firm responds to the regulator's accessing technology by increasing its audit rate. Corollary 1 may seem counterintuitive to those who argue that firms would audit more if access were denied, thereby eliminating the possibility of self-incrimination. However, such an argument must be based on the presumption that the regulator's audit strategy would remain constant despite changes in the regulatory environment. If so, the firm might find it beneficial to audit' more (or less). But, the regulator would surely make adjustments in its audit policy as a response to the firm's new incentives. Only an equilibrium analysis (such as presented here) can consider the reactions of both parties simultaneously.

4.2 Effect of Conditional Penalty The effect of changing the current penalty structure to a conditional penalty structure can be assessed by comparing Scenarios 1 and 3, which vary the penalty assumption but hold constant the regulator's right to access. The debate in the current literature centers around the conjecture that, if the penalty for environmental non-compliance is reduced for a good-faith effort by the firm, then the firm is more likely to engage in compliance audits (relative to its audit policy given an unconditional penalty). Corollary 2 considers this issue for our setting.

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Corollary 2. (i) Assume C r < [3D, Then, as the magnitude of the difference between V o and Va increases, the set of parameter values that supports equilibria in which the firm includes compliance auditing in its strategy becomes larger. (ii) A conditional penalty has no impact on either the regulator's or the firm's strategies within any pure-strategy equilibria (i.e., equilibria (i) and (ii) of Propositions 1 and 3). Within the mixed-strategy equilibria ((iii) and (iv)), the conditional penalty does not affect the firm's audit strategy. However, in equilibrium (iii), the probability of regulator inspection decreases as the magnitude of the difference between V o and Va increases. The first part of the Corollary 2 points out the fact that the magnitude of V o - Va is important in determining which equilibrium occurs. If the environmental impact of non-compliance has a sufficiently large impact (i.e., Cr < flDr), then policymakers can eliminate the second pure-strategy equilibrium by increasing the difference between V0 and Va. Because the firm never audits in this second pure-strategy equilibrium, the range of conditions for which this equilibrium occurs can be reduced by increasing V0 - Va in the differential penalty. Now, more firms find it advantageous to conduct compliance audits. 21 Thus, even if the firm's probability of compliance auditing is not affected by a conditional penalty, the frequency of compliance auditing can be increased by the policymaker influencing which equilibrium is played. A comparison of Figures 2 and 4 illustrates Corollary 2(i). As in Figure 2, each region of Figure 4 represents a corresponding equilibrium in Proposition 3. The shaded region in Figure 4 represents the area for which some compliance audits would occur under conditional penalties but not under unconditional penalties. Increasing the extent of the differential penalty obviously increases the extent of compliance audits. Within the mixed-strategy equilibria for which the regulator inspects with positive probability, the probability of inspection decreases compared to the benchmark scenario as the difference V0 - Vo increases. This is clearly advantageous to the regulator, as the regulator can ensure that the firm does some compliance auditing and, at the same time, can decrease its own costly inspection effort.

21 For example, situations in which pollution occurs as a one-time event (see footnote 5) result in no auditing by the firm in the b e n c h m a r k setting because clean-up costs do not increase over time. However, with conditional penalties, such firms may have sufficient incentives to conduct audits,

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(audit cost)

cfI

#

II

l~of - % + v o - v~) ~(Df-

C_~)

It It

¢ #

[~Dr

C r (inspectioncost)

Figure 4. Equilibrium regions for Scenario 3.

5. Conclusion In this paper, we have developed a model to study the effects of two policy variables on a firm's environmental compliance auditing program. First, we considered the effect of a regulatory agency's ability to access a firm's environmental audit report and to penalize the firm based on that internally-generated report. In our model, the regulator's right to access unambiguously increased the incentive for the firm to conduct a compliance audit (Corollary 1). The argument that the right to access decreases a firm's audit incentives, due to the possibility of self-incrimination, and therefore that laws restricting that access will increase the incentives of the firm to conduct compliance audits (Moore 1992, p. 40), is not consistent with our analysis. In particular, we found that the supposed beneficial aspects of restricted access are based on partial-equilibrium reasoning which does not consider how the regulator's inspection strategy may change. As a result, the recent legislative initiatives in several states which protect environmental compliance audit reports as confidential business information may be unnecessary or even counterproductive. Indeed, the EPA's response to some of these state protections--to threatened increased frequencies of f e d e r a l / E P A enforcement actions (Cushman 1996, p. A1) - - m a y be an appropriate reaction for a regulator attempting to minimize overall environmental damage and regulatory costs. Of course, the institutional environment of environmental regulation and compliance auditing is much more complex than our model. We captured only a single benefit from compliance audits (early detection and clean-up). Existence of other benefits would provide firms with additional incentives to conduct such audits. In particular, the possibility of third-party

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lawsuits may provide considerable impetus to firms' environmental-compliance efforts. In addition, firms may be concerned with regulatory access because, despite good-faith efforts to prevent pollution, public disclosure of unintended environmental non-compliance can adversely affect corporate reputations. These considerations were not captured by our model. We also considered the effect of a penalty schedule which varies with a firm's good-faith efforts to detect and correct environmental non-compliance. The proposed changes to U.S. sentencing guidelines incorporate exactly this kind of penalty schedule. Several authors (e.g., Anderson 1994, p. 47; Doyle 1992, p. 39) have suggested that if the penalty for environmental non-compliance is reduced for a good-faith effort by a firm, firms are more likely to engage in compliance audits than they would be if the potential penalty were unconditional. In our analysis, the likelihood that the firm includes compliance auditing in its strategy increases because the set of parameter values which support these equilibria becomes larger (Corollary 2). That is, under a conditional penalty structure, more firms would be expected to conduct compliance audits. Helpful commentswere provided by three reviewers, Lauren Kelly,Michael Kirschenheiter, Nahum Melumad,Amir Ziv, and workshopparticipants at ColumbiaUniversityand the 1995 Universityof WashingtonEnvironmentalAccountingConference.

Appendix eROOF OF t~MMA i: If the regulator accesses and the firm has conducted a compliance audit, the expected cost to the regulator from inspecting ( Pl = I), and not inspecting ( Pl = O) are: E R I ( p , = 1) = C,,

and E R I ( pl = O) = O.

If the firm has conducted a compliance audit, it finds and correctl any non-compliance with certainty. Hence, an additional inspection by the regulator simply incurs additional cost, C r, with no corresponding benefit. Therefore, the accessing regulator's dominant strategy is to not inspect if the firm has audited. [] PROOF OF PROPOSITION 1" From Lemma 1, we know that Pl = 0, i.e., the accessing regulator's strategy when the firm has audited is to not inspect. As a preliminary step in the proof of Proposition 1, we determine the accessing regulator's strategy when the firm has not audited. The expected cost to the accessing regulator when the firm has not audited is: E R ( p2)

=

Crp 2 -t- (1 - p2)~Dr.

(A1)

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Taking the derivative of equation (A1) with respect to /o2 yields: OER( P2) ( OP2)

C r - ~D,.

(A2)

Equation (A2) implies that if C~ > ~ D r, then P2 = 0, and if Cr < /3D~, then'p2 = 1 Equilibrium (i): Assume Cr > ~Dr( 02 = 0). The regulator's expected cost is given by equation (1) and the firm's expected cost is given by equation (2). Substituting P2 = 0 in equations (1) and (2), the expected costs to the regulator and firm are: E R = a 81K + (l - ot)81(K + j~Or) + 62C ~ + 3Dr(1 - a ) ( 1

-

81

-

82) ,

(A3)

and EF=

ot(Cf + ~ C o + ~ a ~ V o + ~ 6 2 V o) +

j~82(1

--

Ol)(Of "+"Vo),

(A4)

First-order conditions for cost minimization for the regulator and firm are: 3ER 361

= a K + (1 - a ) ( K + / 3 D r) - /3Dr(1 - a ) = K,

(A5)

OER

362

= C r -/3Dr(l

- a),

(A6)

and 3EF oa = CT + ~ C o + ~ 6 1 V o - ~ 6 2 D f.

(A7)

As K > 0, we have 61 = 0 from equation (A5). We also have 62 = 0 for all values of a(0 ~ a < 1), because the right hand side of equation (A6) is always positive, given C~ > ~ D r. Using 61 = 62 = 0, equation (AT) reduces to: 3EF ,

_ _

3or

= Ci+/3C0

> 0,

implying a = 0 in equilibrium. Thus, if C, > /3Dr, then a = 0, 61 = 0, 62 = 0 and 63 = 1 are equilibrium strategies. (Note that in the derivation of equilibrium, Pl = 0 and P2 0 are based on the out of equilibrium beliefs specified in Proposition 1). Equilibrium (ii): Assume C r "< [3D r and Cf > / 3 ( D r - Co). In this case, P2 = 1 by equation (A2). Substituting P2 = 1 in equations (1) and (2), the expected costs to the regulator and firm are: =

E R = ot 61K +

(1

- a ) 6 1 ( K + Cr)

+ 62C ~ + /3Dr(1 - a ) ( 1

-

61

-

82) ,

(A8)

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and E F = a [ C f + [3Co + [3 81Vo + [3 82V0 ]

+ ( 1 - ot)[3[81(Df + V0) + 82(Dr + I/"0)] .

(A9)

The first-order conditions for cost minimization for the regulator and firm are: OER -= K + (1 - a ) ( C r - [3Dr), (A10) 081 OER

082

= C r --

(1

--

(All)

a)[3Dr,

and OEF da = Cf + [3C o - [3(81 + 8 2 ) D f.

(A12)

By Cf + [3(C 0 - Dr) > 0, O E F / O a > 0 because 81 + 82 < 1. Therefore, O ~ 0 .

Given a = 0, the expected costs for the regulator's strategies are: ERis I =ERI(81= ERIs2 =ERI(82

1) = K + C

r,

= 1) = C ~ ,

and E R I s3 = E R I ( 83 = 1) = flD r.

Because C r < [3Dr, s 2 (/52 = 1) is the dominant strategy. Hence, for C r < [ 3 D r and C f + / 3 ( C o - D r ) > 0 , 8 2 = 1, 81 = 0 , 8 3 = 0 , and oz=-0 are equilibrium strategies. (Note that in the derivation of equilibrium, Pl = 0 and P2 = 1 are based on the out of equilibrium beliefs specified in Proposition 1. Equilibrium (iii): Assume C,. < flD,., Cf < f l ( D f - C o ) ) , and K > Cr([3D r - C,.)/[3D r. By L e m m a 1, Pl = 0 , and by C r <[3Dr, P 2 = 1. Therefore, the first-order conditions given by equations (A10), ( A l l ) , and (A12) apply. Suppose the agent's strategy is a = 1 - Cr/[3Dr. Then, by the regulator's first-order condition (A10) and C,.([3D,.- C r) < [3DrK, we have O E R / 0 8 1 > 0, implying 8 1 = 0. Again, substituting the agent's strategy into the regulator's first-order condition ( A l l ) , and using Cf + [3(C o - Dr) < 0, we can solve equation (A12) for 8 2 : (Cf + [ 3 C o ) / [ 3 D f < 1. Using /51 = 0 and 8 2 = (Cf + [3Co)//[3Of, we can solve equation ( A l l ) for a = 1 - C,./[3D,.. Thus, a = 1 - C,./[3Dr, 81 = O, 8 2 = (Cf + [3C0)/[3D f, and 8 3 = 1 8 1 a r e equilibrium strategies. (Note that in the derivation of equilibrium, /91 = 0 and /92 = 1 are based on the out of equilibrium beliefs specified in Proposition 1.)

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Equilibrium (iv): Assume C~ < [3Dr, Cf < [ 3 ( D f - C O) and K < Cr( [3Dr -- C~)/[3Dr. By L e m m a 1,

P l = 0, and by C~ < r i D , P2 = 1. Therefore, the first-order conditions given by equations (A10), ( A l l ) , and (A12) apply. Using a = 1 - K / ( [ 3 D r - Cr) (the firm's equilibrium strategy) and C r ( flD r -- C r) > flD~K, we have a E R / 0 8 2 > 0, which implies 62 = 0. Using 62 --- 0 and Cf + fl(C o - Dr) < 0, equation (A12) implies 61 =

(C: + f l C o ) / ~ D f < 1. Finally, using 62 = 0 and 61 = (C r + [3Co)/[3D p equation (A10) can be solved for a - 1 - K / ( [3D~ - C~). Thus, a = 1 - K / ( [3Dr - C~), 01 = O, P2 = 1, 61 = (Cf + ~Co)/[3Df, 62 = 0, and 33 = 1 - 6 t are equilibrium strategies. [] 2: In the no-access, unconditional penalty setting, the game can be modeled as simultaneous play. Therefore, we derive the Nash equilibria of the game. The regulator's expected cost is given by equation (3) and the firm's expected cost is given by equation (4). The first-order conditions for expected cost minimization are: PROOF OF PROPOSITION

OER -ay

= Cr - (1 - ct)flD~,

(A13)

flyDf.

(A14)

and

OEF Oa

= Cf + ~C o -

Equilibrium (i): Assume Cr > [3Dr. Then a E R / a y > 0 for any a [0, 1], and y = 0 is a dominant strategy for the regulator. Given y = 0, O E R / a a > 0, implying that the firm's best response is a = 0. Therefore, y = 0 and a = 0 represent equilibrium strategies. Equilbrium (ii): Assume C~ < flD, and C / > fl(Df - Co). T h e n a E F / a a > 0, implying that the firm's dominant strategy is a = 0. Given a = 0 and C, < flDr, a E R / a y < 0, implying that the regulator's best response is y = 1. Therefore, y = 1 and a = 0 represent equilibrium strategies. Equilibrium (iii): Assume Cr < flD, and C / < [ 3 ( D / - Co). Given a = 1 - C,/[3D,, the regulator's best response is given by solving equation (A14): y = (C: + [3Co)/[3D f, where y < 1 by C / + [3(C o - Dr) < 0. Similarly, given y = (Cf + flCo)/[3D f, the firm s best response is given by solving equation (A13): a = 1 - Cr/[3D,., where a > 0 by C, < flD,. Therefore, y = ( C / + [3Co)/[3D / and a = 1 - C,/[3D, represent equilibrium strategies. []

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PROOF OF PROPOSITION 3: The regulator's expected cost in the setting with access and a conditional penalty structure is identical to the benchmark setting. Therefore, as in Proposition 1, we know that the accessing regulator's strategy is given by Pl = 0 (by Lemma 1) and P2 = 0 if C, > r D , , and P2 = 1 if C r < r D , (proof in Proposition 1). The regulator's expected cost in the setting with access and a conditional penalty structure is given by equation (1) and the firm's expected cost is given by equation (5). E q u i l i b r i u m (i): Assume C r > BID,. Substituting P2 = 0 in equations (1) and (5) yields the regulator's and firm's expected costs: E R = a 81K + (1

-

a)81(K

flD r)

+

+ 82C r + r D r ( 1 - a ) ( 1

-

81 -- 82) ,

(A15)

and

E F = a [ C f + r C o + / 3 alVa q'- r 82va]

+(1 - a ) r S z ( D f + Iio).

(A16)

The first-order conditions for cost minimization for the regulator and firm are: OER = c~K + (1 - a ) ( K + /3/9,) - /3/9,(1 - a ) = K ,

381

OER - = C~ - r D r ( 1 - ct),

082

(A17)

(A18)

and

OEF

da

= Cf + r c 0 + fl(81 + 82)va - r 8 2 ( v 0 + Dr).

(A19)

As K > 0, we have 81 = 0. We also have 82 = 0 for all values of a(0 _< a _< 1), because the right hand side of equation (A18) is always positive, given C, > r D , . Using 81 = 82 ~---0, equation (A19) becomes: OEF Oa = c f + r c 0 > 0 ,

implying a = 0 in equilibrium. Thus if C, > r D , , then a = 0, 81 = 0, 82 = 0 a n d 83 = 1 are equilibrium strategies. Equilibrium (ii)-(iv):

A s s u m e Cr < r D , ( Pa = 1). S u b s t i t u t i n g P2 = 1

in equations (1) and (5) yields the regulator's and firm's expected costs: E R = a 81K + (1 - a ) 8 1 ( K + C r)

+ 82C , + flDr(1 - a ) ( 1 - 81 - 82),

(A20)

and E F = a ( C f + t i C o + fl ~lVa + fl

+(1 - a ) r [ 8 1 ( D f +

~2Va)

V o) + 8 2 ( D r + 1,1o)].

(A21)

B.K. Mishra et al.

212

The first-order conditions for cost minimization for the regulator and firm are: OER

-= K + (1 - a ) ( C r - flDr), 06a OER

-= C ~ - (1 062

-

ot)flDr,

(A22)

(A23)

and OEF 00l

= C f -[- [ 3 C 0 -

f l ( 6 1 -{- 6 2 ) ( V 0 - Va -J- D / ) .

(A24)

Note that conditions (A22), (A23), and (A24) are identical to conditions (A10), ( A l l ) , and (A12) in Proposition 1 if we substitute D 7 for (V0 :Va + Dr). Using this identity, we know that the equilibria for the modified game when C r < flD r are: (ii) If C r < f l D r and C f > f l ( D T - C 0 ) , then 6 1 = 6 3 = a = 0 and 6 2 = 1. (iii) If C r < ~ D r, Cf < fl(D~ - C 0) and g > Cr( flD r - C r ) / f l D ~, then 62=(Cf+flCo)/flD ~, 61 = 0 , 6 3 = 1 - 62 and ot

=

1

-

C r / f l O r.

(iv) If Cr < BDr, C r < ~ ( D ~ - Co) and K < Cr( flD~ - C r ) / f l D . then Pa = O, P2 = 1, 61 = ( C f + f l C o ) / f l D ~, 62 = 0, 6 3 = 1 - 61 and a = 1 - K / ( ~D~ - Cr).

To convert these equilibria to the ones stated in Proposition 3, substitute ( V o - V ~ + Dr) for /)7. (In equilibria (i), (ii), and (iii), the accessing regulator's conditional strategies (Pl and P 2 ) a r e based on the out of equilibrium beliefs specified in Proposition 3 (because for these equilibria, the regulator never accesses).) [] PROOF OF COROLLARY 1: Compare equilibrium (iv) (Proposition 1) of the benchmark model with equilibrium (iii) (Proposition 2). Each of these equilibria will occur given the conditions posited (C~ < ~Dr, Cf < ~ ( D I Co) and K < C,~( flD, - C , ) / ~ D r ) . T h e probability of an audit by the firm in the benchmark model is a = 1 - K / ( ~ D r - C ~ ) . In the no-access model, the probability of an audit is a = 1 - C J f l D r. Thus, if 1 - K / ( f l D r - C r) > 1 - C r / ~ D r, the probability that the firm will conduct a compliance audit is greater in the benchmark model. But, 1 -K/(BD,G ) > 1 - C r / B D , is equivalent to K < C~(/3D r C r ) / f l D . which is true by assumption. [] PROOF OF COROLLARY 2: (i) Assume Cr < ~Dr. Then, as V0 - V~ increases, the set of parameters for which Cf + ~Co - ~(Vo - V,, + Dr) > 0

Environmental Compliance Audits

213

holds becomes smaller. That is, the parameter space for which equilibrium (ii) (in which the firm never audits) occurs is reduced and the parameter space for which equilibria (iii) and (iv), in which the firm audits with positive probability, becomes larger. (ii) The proof is straightforward frotp a comparison of the regulator's and firm's strategies in the four equilibria for the benchmark and conditional penalty models. []

References Anderson, U. Spring 1994. The new federal sentencing guidelines: Implications for the internal audit function, lnternal Auditing 10(1):46-50. Campbell, S. N. and Byington, J. R. Fall 1995. Environmental auditing: An environmental management tool. Internal Auditing 11(2):9-18. CH2M Hill. 1993. The Role of lnternal Auditors in Environmental Issues. Altamonte Springs, FL: The Institute of Internal Auditors Research Foundation. Companies wary of use of environmental audits. Apr. 17, 1995. Oil & Gas Journal 93(16):25. Cushman, J. H., Jr. Apr. 7, 1996. Many states give polluting firms new protections. The New York Times 146(50,380):A1, A12. Doyle, J. Jan./Feb. 1992. Audits are their own reward. The Environmental Forum 9(1):38-39. Enviro auditing: EPA opposition squelches some state bills. June 12, 1996. Greenwire 6(30):1, Environmental Protection Agency (EPA). Apr. 3, 1995a. Voluntary environmental self-policing and self-disclosure interim policy statement. Federal Register 60(63): 16875- 16879. Environmental Protection Agency (EPA). Dec. 22, 1995b. Incentives for self-policing: Discovery, disclosure, correction and prevention of violations. Federal Register 60(246):66706-66712. Fairley, P. May 29, 1996. EPA defends policy, opposes legislation. Chemical Week 158(21):13. Florida: Biz self-audit bill stalls, but may come up again. Mar. 28, 1996. Greenwire 5(222):14. Fudenberg, D. and Tirole, J. 1991. Game Theory. Cambridge: MIT Press. Manko, J. M. and Gilsford, M. J. Winter 1991/1992. Enforcement trends: DOJ policy on prosecutorial discretion. Journal of Environmental Regulation 1(4): 225-232. Michigan: State firms cite high enviro compliance costs. Feb. 7, 1997. Greenwire. 6(188):18. Mokhiber, R. Oct. 15, 1995. Don't hinder pollution police. The New York Times 145(50,215):Cll. Moore, J. R. Jan./Feb. 1992. Protection will increase compliance. The Environmental Forum 9(1):39-41.

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Morelli, J. A. Feb. 1994. Performing environmental audits: An engineer's guide. Chemical Engineering 101(2):104-113. Schaltegger, S. and Stinson, C. H. 1994. Issues and research opportunities in environmental accounting. WWZ Discussion Papers Nr. 9423. Basel, Switzerland: Universit~it Basel. Tihor, T. and Feldman, I. 1996. ISO 14000:.4 Guide to the New Environmental Management Standards. Chicago: Irwin Professional Publishing.